Question 1: A Lotto Money

One of the largest lottery jackpots ever won was on March 27, 2019. The winning numbers for the $768,400,000 jackpot in Americas biggest lottery game, Powerball, were on a single winning ticket sold in Wisconsin. The Powerball rules gave the winner a choice between receiving 30 graduated annual payments totalling $748.4 million (including one immediately) or an immediate lump payment of $477 million.

A.) If the Powerball winners can earn 6% compounded annually on their personal investments, what was the initial economic value of the annuity to them? Which option should they have chosen in that case?

Question 2: Savings from a shorter Amortization Period

AN ANALYSIS OF THE INTEREST SAVINGS FROM CHOOSING A SHORTER AMORTIZATION PERIOD

Amortization period Monthly payment ($) Total of all payments ($) Total interest ($)

25 years $596.30 $178,890 $78,890

20 years $671.05 $161,052 $61,052

Difference: (74.75) 17,838 17,838

Many financial planners and commentators make a great ballyhoo about the large amount of interest that can be saved by choosing a shorter mortgage amortization period. Their typical analysis goes as follows. (We will use monthly compounding rather than semiannual compounding to simplify the math.) Suppose you obtain a $100,000 mortgage loan at 5.2% compounded monthly. The following table compares 20- and 25-year amortizations.

Source: CMHC.

By choosing a 20-year amortization, you will have interest savings of $17,838. The savings result from eliminating payments of $596.30 per month during Years 21 to 25 by spending an extra $74.75 per month during Years 1 to 20. That is,n Interestsaving = (512$596.30)(2012$74.75)=$17,838

It seems quite astoundingincreasing the monthly mortgage payment by a little more than 12% reduces the total interest costs by over 22%! The usual conclusion is that reduction of your mortgages amortization period should be one of your highest financial priorities because of the amazing interest savings. In the present example, you will be $17,838 ahead by choosing the 20-year amortization.

Do you see any flaws in this conventional analysis? Is it complete? Does it violate any basic concept you have learned?

The main flaw in the analysis is that a basic concept in financethe time value of moneyhas been ignored. Whenever you add nominal dollar amounts that are paid on different dates, you are ignoring the time value of money. The longer the time frame over which the payments are spread, the more serious the resulting error will be. In the preceding analysis, a dollar in Year 25 is treated as having the same value as a dollar in Year 1. In fact, individual dollars saved in Years 21 to 25 have, on average, significantly less economic value than extra dollars spent in Years 1 to 20. Let us do a rigorous analysis to determine the amount of the economic advantage of the shorter amortization period.

Questions:

1. For the first 20 years, the monthly payments on the 25-year amortization are $74.75 lower than the payments on the 20-year amortization loan. Suppose you invest this difference each month to earn the same rate of interest that you pay on either mortgage. How much will you accumulate after 20 years?

Question:

A company is evaluating two mutually exclusive projects. Both require an initial investment of $250,000 and have no appreciable disposal value. Their expected profits over their five-year lifetimes are as follows:

Year Project Alpha ($) Project Beta ($)

1 $120,000 $20,000

2 $80,000 $40,000

3 $60,000 $60,000

4 $20,000 $100,000

5 $20,000 $120,000

The companys cost of capital is 7%. Calculate the NPV (Net Present Value) and IRR (Interest Rate of Return) for each project. Which project should be chosen? Why?